NLMS Step Size Question

I'm running into difficulty implementing the NLMS algorithm, w.r.t.
step size..

I'm using Matlab to model the algorithm, and here is the core of the
calculation to update the tap weights:

nlms_coeff = af_parms.mu/pwr(i) * en;
af_parms.state.weights = af_parms.state.weights +  xn .* nlms_coeff;

- pwr(i) is the calculated signal power for sample 'i'
- xn is the data samples used for 'L' taps (1024 in this case).
- I am using step-size of 0.2

Now, the problem arises when I change how pwr(i) is calculated.

If I use pwr(i) = xn' * xn , which is essentially the sum of squared
elements, the algorithm works perfectly.

I want to use a power estimate however, described in TI's application
note spra063.pdf. This uses an IIR filter of the form:

pwr(i) = (1-alpha_s)*pwr(i-1) + alpha_s*(wave_src(i)^2);

where alpha_s = short-term time constant 1/128, and wave_src(i) is the
current input sample.

If I use this method for pwr(i), the algorithm blows up and spits out
garbage (really large values). I tried dropping the step size from 0.2
to 2^-10, and that didn't seem to make a difference.

Plotting the two methods of calculating pwr against eachother, they
seem to follow the same trend, however the power 'estimate' is
definitely scaled down by a factor of around 1000. I tried taking this
into account in adjusting the weights, howevre, it still does not
work.

Any ideas?

On Nov 5, 7:24 pm, "jai.d...@gmail.com" <jai.d...@gmail.com> wrote:
> I'm running into difficulty implementing the NLMS algorithm, w.r.t.
> step size..
>
> I'm using Matlab to model the algorithm, and here is the core of the
> calculation to update the tap weights:
>
> nlms_coeff = af_parms.mu/pwr(i) * en;
> af_parms.state.weights = af_parms.state.weights +  xn .* nlms_coeff;
>
> - pwr(i) is the calculated signal power for sample 'i'
> - xn is the data samples used for 'L' taps (1024 in this case).
> - I am using step-size of 0.2
>
> Now, the problem arises when I change how pwr(i) is calculated.
>
> If I use pwr(i) = xn' * xn , which is essentially the sum of squared
> elements, the algorithm works perfectly.
>
> I want to use a power estimate however, described in TI's application
> note spra063.pdf. This uses an IIR filter of the form:
>
> pwr(i) = (1-alpha_s)*pwr(i-1) + alpha_s*(wave_src(i)^2);
>
> where alpha_s = short-term time constant 1/128, and wave_src(i) is the
> current input sample.
>
> If I use this method for pwr(i), the algorithm blows up and spits out
> garbage (really large values). I tried dropping the step size from 0.2
> to 2^-10, and that didn't seem to make a difference.
>
> Plotting the two methods of calculating pwr against eachother, they
> seem to follow the same trend, however the power 'estimate' is
> definitely scaled down by a factor of around 1000. I tried taking this
> into account in adjusting the weights, howevre, it still does not
> work.
>
> Any ideas?

The canonical form of Normalized LMS (NLMS) scales the stepsize by the
power of the tap-input vector to keep the adaptation bandwidth
constant across variations in the input signal, which is exactly what
you're doing when you use xn' * xn. Doing a dot product on a 1024
element vector is computationally expensive though, so you'd like to
find a simpler way to estimate power.

When you use the TI power approximation with a simple mag^2 and IIR
filter, you have to choose the alpha_s time constant to constrain the
power calculation to a time period equivalent to the length of the tap-
input vector. Otherwise, you risk discarding the contribution of some
elements, or allowing an influence from elements beyond the current
set. Also, you note a scale difference between the dot product and the
square/filter technique which will certainly affect the value of
af_parms.mu which you use for the two approaches.

EB

That was an excellent explanation, thanks!

 I changed the alpha parameter to my tap size (1024), and then reduced
the Mu parameter to around 2^-10, and it works perfectly!

J

On Nov 6, 11:48 am, emeb <ebromba...@gmail.com> wrote:
> On Nov 5, 7:24 pm, "jai.d...@gmail.com" <jai.d...@gmail.com> wrote:
>
>
>
> > I'm running into difficulty implementing the NLMS algorithm, w.r.t.
> > step size..
>
> > I'm using Matlab to model the algorithm, and here is the core of the
> > calculation to update the tap weights:
>
> > nlms_coeff = af_parms.mu/pwr(i) * en;
> > af_parms.state.weights = af_parms.state.weights +  xn .* nlms_coeff;
>
> > - pwr(i) is the calculated signal power for sample 'i'
> > - xn is the data samples used for 'L' taps (1024 in this case).
> > - I am using step-size of 0.2
>
> > Now, the problem arises when I change how pwr(i) is calculated.
>
> > If I use pwr(i) = xn' * xn , which is essentially the sum of squared
> > elements, the algorithm works perfectly.
>
> > I want to use a power estimate however, described in TI's application
> > note spra063.pdf. This uses an IIR filter of the form:
>
> > pwr(i) = (1-alpha_s)*pwr(i-1) + alpha_s*(wave_src(i)^2);
>
> > where alpha_s = short-term time constant 1/128, and wave_src(i) is the
> > current input sample.
>
> > If I use this method for pwr(i), the algorithm blows up and spits out
> > garbage (really large values). I tried dropping the step size from 0.2
> > to 2^-10, and that didn't seem to make a difference.
>
> > Plotting the two methods of calculating pwr against eachother, they
> > seem to follow the same trend, however the power 'estimate' is
> > definitely scaled down by a factor of around 1000. I tried taking this
> > into account in adjusting the weights, howevre, it still does not
> > work.
>
> > Any ideas?
>
> The canonical form of Normalized LMS (NLMS) scales the stepsize by the
> power of the tap-input vector to keep the adaptation bandwidth
> constant across variations in the input signal, which is exactly what
> you're doing when you use xn' * xn. Doing a dot product on a 1024
> element vector is computationally expensive though, so you'd like to
> find a simpler way to estimate power.
>
> When you use the TI power approximation with a simple mag^2 and IIR
> filter, you have to choose the alpha_s time constant to constrain the
> power calculation to a time period equivalent to the length of the tap-
> input vector. Otherwise, you risk discarding the contribution of some
> elements, or allowing an influence from elements beyond the current
> set. Also, you note a scale difference between the dot product and the
> square/filter technique which will certainly affect the value of
> af_parms.mu which you use for the two approaches.
>
> EB